Finite Group Databasebeta

← #7647197

Subgroups — #7647197

Order 512.

8600 conjugacy classes of subgroups.

The subgroup lattice has 1104 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3505C211yesmaximal, characteristic, complemented
2C22×#550C211yesmaximal, characteristic, complemented
3#40605C218yesmaximal, complemented
4#40601C218yesmaximal, complemented
5#38093C214yesmaximal, complemented
6#38089C214yesmaximal, complemented
7#37683C214yesmaximal, complemented
8#37681C214yesmaximal, complemented
9#37614C212yesmaximal, complemented
10#37451C211yesmaximal, characteristic, complemented
11#37450C211yesmaximal, characteristic, complemented
12#37232C214yesmaximal, complemented
13#36706C214yesmaximal, complemented
14#35355C214yesmaximal, complemented
15#35305C211yesmaximal, characteristic, complemented
16#35250C211yesmaximal, characteristic, complemented
17#35246C212yesmaximal, complemented
18#35078C212yesmaximal, complemented
19#34987C214yesmaximal, complemented
20#34738C212yesmaximal, complemented
21#34057C211yesmaximal, characteristic, complemented
22C23×#41C2211yescharacteristic
23C23×#41C2211yescharacteristic, complemented
24#3505—216no—
25C2×#553C2214yescomplemented
26C2×#553C2212yescomplemented
27C2×#552C2212yescomplemented
28C2×#551C2214yescomplemented
29C2×#550—216no—
30C2×#550C2214yes—
31C2×#550C2214yes—
32C2×#550C2214yescomplemented
33C2×#550C2214yescomplemented
34C2×#548C2212yescomplemented
35C2×#546C2212yescomplemented
36C2×#539C2212yes—
37C2×#538C2212yes—
38C2×#536C2212yescomplemented
39C2×#535C2212yescomplemented
40C2×#534C2212yes—
41C2×#532C2214yescomplemented
42C22×#127C2212yes—
43C22×#127C2211yescharacteristic, complemented
44C2×#529C2212yes—
45C2×#525C2212yes—
46C22×C22⋊Q8C2211yescharacteristic
47C22×#121C2212yes—
48C22×#121C2211yescharacteristic
49C22×#121C2211yescharacteristic
50C22×#121C2211yescharacteristic, complemented
51C22×#121C2212yescomplemented
52C2×#518C2212yes—
53C22×C4×Q8C2211yescharacteristic, complemented
54C22×C4×D4C2211yescharacteristic
55C22×C4×D4C2212yescomplemented
56#2856C2214yescomplemented
57#2853C2218yescomplemented
58#2850C2214yescomplemented
59#2848C2214yescomplemented
60#2847C2214yes—
61#2818C2218yescomplemented
62#2816C2214yescomplemented
63#2815C2214yescomplemented
64#2709C22116yescomplemented
65#2691C22116yescomplemented
66#2676C22116yescomplemented
67#2675C22116yescomplemented
68#2673C22116yescomplemented
69#2673C22116yescomplemented
70#2671C22116yescomplemented
71#2669C22116yescomplemented
72#2661C2218yescomplemented
73#2657C2214yescomplemented
74#2641C2214yescomplemented
75#2637C2218yescomplemented
76#2626C2214yescomplemented
77#2620C2214yescomplemented
78#2619C2214yescomplemented
79#2619C2218yescomplemented
80#2618C2214yescomplemented
81#2617C2214yes—
82#2617C2214yescomplemented
83#2616C2214yescomplemented
84#2615C2214yescomplemented
85#2613C2218yescomplemented
86#2599C2218yescomplemented
87#2579C2218yescomplemented
88#2565C2214yescomplemented
89#2548C2214yescomplemented
90#2545C2214yescomplemented
91#2543C2218yescomplemented
92#2541C2214yescomplemented
93#2504C2212yes—
94#2504C2212yescomplemented
95#2502C2212yescomplemented
96#2501C2212yescomplemented
97#2500C2214yescomplemented
98#2476C22116yescomplemented
99#2467C22116yescomplemented
100#2464C22116yescomplemented
101#2463C22116yescomplemented
102#2460C22116yescomplemented
103#2456C22116yescomplemented
104#2456C22116yescomplemented
105#2436C2212yes—
106#2436C2212yescomplemented
107#2435C2212yescomplemented
108#2435C2212yescomplemented
109#2434C2212yescomplemented
110#2433C2212yes—
111#2433C2212yes—
112#2433C2212yescomplemented
113#2432C2214yescomplemented
114#2432C2214yescomplemented
115#2431C2214yescomplemented
116#2431C2214yescomplemented
117#2431C2214yescomplemented
118#2430C2218yescomplemented
119#2424C22116yescomplemented
120#2410C2218yescomplemented
121#2410C2218yescomplemented
122#2408C2218yescomplemented
123#2406C2214yescomplemented
124#2405C2214yes—
125#2405C2214yes—
126#2404C2214yescomplemented
127#2403C2214yes—
128#2403C2214yes—
129#2388C2218yescomplemented
130#2327C2214yescomplemented
131#2326C2214yescomplemented
132#2321C2218yescomplemented
133#2318C2214yescomplemented
134#2318C2214yescomplemented
135#2315C2212yescomplemented
136#2313C2212yescomplemented
137#2312C2212yes—
138#2311C2212yescomplemented
139#2311C2212yescomplemented
140#2308C2212yes—
141C4×#120C2218yescomplemented
142#2297C2214yescomplemented
143#2290C2214yescomplemented
144#2290C2214yescomplemented
145#2283C2212yescomplemented
146#2280C2211yescharacteristic
147#2280C2211yescharacteristic
148C2×C4×C22⋊C4C2212yescomplemented
149C22×#41—28no—
150C22×#41—28no—
151C22×#41—48no—
152C22×#41—48no—
153C22×#41C2312yes—
154C22×#41C2312yes—
155C22×#41C2314yes—
156C22×#41C2312yes—
157C22×#41C2312yes—
158C22×#41C2314yes—
159C22×#41C2312yes—
160C23×Q8C2311yescharacteristic
161C23×Q8C2311yescharacteristic
162C23×D4C2312yes—
163C23×D4C2311yescharacteristic
164C23×D4C2311yescharacteristic
165C23×D4C2312yes—
166C23×D4C2312yes—
167C23×D4C2312yes—
168C23×D4C2311yescharacteristic
169C23×D4C2312yes—
170C23×D4C2312yes—
171C23×D4C2312yes—
172C23×D4C2311yescharacteristic
173C24×C4C2312yes—
174C24×C4C2312yes—
175C24×C4C2311yescharacteristic
176C24×C4C2311yescharacteristic
177#553—216no—
178#553—232no—
179#552—216no—
180#551—232no—
181#550—232no—
182#550—232no—
183#550—232no—
184#550—232no—
185#548—216no—
186#546—216no—
187#539—216no—
188#538—216no—
189#536—48no—
190#535—48no—
191#534—216no—
192#532—416no—
193C2×C4⋊Q8C2314yes—
194C2×#127—216no—
195C2×#127—28no—
196C2×#127C2314yes—
197C2×#127C2314yes—
198C2×#127C2318yes—
199C2×#127C2318yes—
200C2×#127C2314yes—
201C2×#127C2314yes—
202#529—216no—
203C2×#126C2314yes—
204C2×#126C2314yes—
205C2×#126C2314yes—
206C2×#125C2312yes—
207C2×#125C2314yes—
208C2×#124C2314yes—
209C2×#124C2312yes—
210C2×#124C2314yes—
211C2×#124C2314yes—
212C2×#124C2314yes—
213#525—216no—
214C2×#123C2314yes—
215C2×#123C2314yes—
216C2×#123C2314yes—
217C2×#123C2314yes—
218C2×#123C2314yes—
219C2×#123C2318yes—
220C2×#123C2318yes—
221C2×C22⋊Q8—28no—
222C2×C22⋊Q8C2312yes—
223C2×C22⋊Q8C2312yes—
224C2×C22⋊Q8C2312yes—
225C2×C22⋊Q8C2312yes—
226C2×C22⋊Q8C2312yes—
227C2×C22⋊Q8C2314yes—
228C2×C22⋊Q8C2318yes—
229C2×#121—28no—
230C2×#121—28no—
231C2×#121—28no—
232C2×#121—216no—
233C2×#121—216no—
234C2×#121C2312yes—
235C2×#121C2312yes—
236C2×#121C2314yes—
237C2×#121C2312yes—
238C2×#121C2312yes—
239C2×#121C2312yes—
240C2×#121C2312yes—
241C2×#121C2312yes—
242C2×#121C2312yes—
243C2×#121C2314yes—
244C2×#121C2312yes—
245C2×#121C2318yes—
246C2×#121C2318yes—
247C2×#121C2318yes—
248C2×#121C2318yes—
249C2×#121C2314yes—
250C2×#121C2314yes—
251C2×#121C2314yes—
252C2×#121C2318yes—
253C2×#121C23116yes—
254C2×#121C23116yes—
255C2×#121C23116yes—
256C2×#120C2314yes—
257C2×#120C2314yes—
258C2×#120C2318yes—
259C2×#120C2318yes—
260C2×#120C2318yes—
261C2×#120C2318yes—
262#518—216no—
263C2×C4×Q8—28no—
264C2×C4×Q8C2314yes—
265C2×C4×Q8C2312yes—
266C2×C4×Q8C2314yes—
267C2×C4×D4—216no—
268C2×C4×D4D4116yescomplemented
269C2×C4×D4C2314yes—
270C2×C4×D4C2314yes—
271C2×C4×D4C2312yes—
272C2×C4×D4C2314yes—
273C2×C4×D4C2318yes—
274C2×C4×D4C2318yes—
275C2×C4×D4C2314yes—
276C2×C4×D4C2314yes—
277C2×C4×D4C23116yes—
278C2×C4×D4C2312yes—
279C2×C4×D4C2312yes—
280C2×C4×D4C2312yes—
281C2×C4×D4C2312yes—
282C2×#117C2314yes—
283C2×#117C2314yes—
284C2×#117C2312yes—
285C2×#117C2312yes—
286C2×#117C2312yes—
287C22×C4⋊C4C2311yescharacteristic
288C22×C4⋊C4C2311yescharacteristic
289C22×C4⋊C4C2312yes—
290C22×C4⋊C4C2312yes—
291C22×C4⋊C4C2311yescharacteristic
292C22×C4⋊C4C2311yescharacteristic
293C22×C22⋊C4C2312yes—
294C22×C22⋊C4C2312yes—
295C22×C22⋊C4C2312yes—
296C22×C22⋊C4C2312yes—
297C22×C22⋊C4C2314yes—
298C22×C22⋊C4C2314yes—
299C22×C22⋊C4C2311yescharacteristic
300C22×C22⋊C4C2311yescharacteristic
301C22×C42C2312yes—
302C22×C42C2314yes—
303C22×C42C2311yescharacteristic
304#399C2318yes—
305#398C2318yes—
306#398C23116yes—
307#397C2318yes—
308#397C2318yes—
309#396C23116yes—
310#396C23116yes—
311#395C2318yes—
312#394C2318yes—
313#394C23116yes—
314#394C23116yes—
315#394C2318yes—
316#394C23116yes—
317#394C23116yes—
318#394C23116yes—
319#394C23116yes—
320#394C23116yes—
321#394C23116yes—
322#393C2318yes—
323#393C2318yes—
324#392C23116yes—
325#392C2318yes—
326#392C2318yes—
327#392C23116yes—
328#392C23116yes—
329#392C23116yes—
330#392C2318yes—
331#392C23116yes—
332#392C23116yes—
333#392C23116yes—
334#391C2314yes—
335#391C2314yes—
336#391C2314yes—
337#390C2314yes—
338#390C2314yes—
339#390C23116yes—
340#390C2314yes—
341#390C2314yes—
342#390C23116yes—
343#390C2314yes—
344#388C2318yes—
345#388C2318yes—
346#388C23116yes—
347#388C23116yes—
348#388C23116yes—
349#388C23116yes—
350#387C23116yes—
351#387C2318yes—
352#387C2318yes—
353#387C23116yes—
354#387C23116yes—
355#386C2318yes—
356#386C2318yes—
357#386C2318yes—
358#386C2318yes—
359#386C2318yes—
360#386C23116yes—
361#386C2318yes—
362#386C23116yes—
363#386C23116yes—
364#386C2318yes—
365#386C2318yes—
366#386C23116yes—
367#386C23116yes—
368#385C2318yes—
369#385C2318yes—
370#385C2318yes—
371#385C23116yes—
372#385C2318yes—
373#385C23116yes—
374#385C23116yes—
375#384C2314yes—
376#383C2314yes—
377#382C2314yes—
378#382C2314yes—
379#381C2312yes—
380#381C2314yes—
381#381C2312yes—
382#380C2318yes—
383#380C2318yes—
384#380C2314yes—
385#380C2312yes—
386#380C2312yes—
387#380C2312yes—
388#380C2312yes—
389#379C2312yes—
390#379C2312yes—
391#379C2318yes—
392#379C2318yes—
393C4×C4⋊C4C2314yes—
394C4×C22⋊C4C2314yes—
395C4×C22⋊C4C2314yes—
396C4×C22⋊C4C23116yes—
397C4×C22⋊C4C2314yes—
398C4×C22⋊C4C2312yes—
399C4×C22⋊C4C2312yes—
400C4×C22⋊C4C2312yes—
401C4×C22⋊C4C2312yes—
402#376C2314yes—
403C2×#95C2314yes—
404C25C2412yes—
405C25C2412yes—
406C25C2411yescharacteristic
407C25C2411yescharacteristic
408C25C2412yes—
409C2×#41—216no—
410C2×#41—28no—
411C2×#41—28no—
412C2×#41—28no—
413C2×#41—28no—
414C2×#41—216no—
415C2×#41—28no—
416C2×#41—28no—
417C2×#41—216no—
418C2×#41—28no—
419C2×#41—48no—
420C2×#41—44no—
421C2×#41—44no—
422C2×#41—416no—
423C2×#41—48no—
424C2×#41—48no—
425C2×#41—48no—
426C2×#41—464no—
427C2×#41—464no—
428C22×Q8—28no—
429C22×Q8—24no—
430C22×Q8—24no—
431C22×Q8—44no—
432C22×Q8C2412yes—
433C22×Q8C2412yes—
434C22×Q8C2412yes—
435C22×Q8C2412yes—
436C22×D4—28no—
437C22×D4—28no—
438C22×D4—28no—
439C22×D4—28no—
440C22×D4—28no—
441C22×D4—28no—
442C22×D4—24no—
443C22×D4—24no—
444C22×D4—28no—
445C22×D4—24no—
446C22×D4—48no—
447C22×D4—48no—
448C22×D4—44no—
449C22×D4—44no—
450C22×D4—44no—
451C22×D4—44no—
452C22×D4—48no—
453C22×D4—48no—
454C22×D4—84no—
455C22×D4—84no—
456C22×D4—84no—
457C22×D4C2×D418yes—
458C22×D4C2414yes—
459C22×D4C2412yes—
460C22×D4C2412yes—
461C22×D4C2412yes—
462C22×D4C2414yes—
463C22×D4C2418yes—
464C22×D4C2414yes—
465C22×D4C2414yes—
466C22×D4C2418yes—
467C22×D4C2414yes—
468C22×D4C2414yes—
469C22×D4C2414yes—
470C22×D4C2412yes—
471C22×D4C2418yes—
472C22×D4C2418yes—
473C22×D4C2414yes—
474C22×D4C2412yes—
475C22×D4C2412yes—
476C22×D4C24116yes—
477C22×D4C24116yes—
478C22×D4C2412yes—
479C22×D4C2412yes—
480C23×C4—28no—
481C23×C4—28no—
482C23×C4—44no—
483C23×C4—44no—
484C23×C4—48no—
485C23×C4—48no—
486C23×C4C2×D418yes—
487C23×C4C2×D418yes—
488C23×C4C2412yes—
489C23×C4C2418yes—
490C23×C4C2414yes—
491C23×C4C2414yes—
492C23×C4C2411yescharacteristic
493C23×C4C2411yescharacteristic
494C23×C4C2411yescharacteristic
495C23×C4C2411yescharacteristic
496C23×C4C2412yes—
497C23×C4C2412yes—
498C23×C4C2412yes—
499C23×C4C2412yes—
500C23×C4C2412yes—
501C23×C4C2414yes—
502C23×C4C2414yes—
503C23×C4C2418yes—
504C23×C4C2411yescharacteristic
505C23×C4C2411yescharacteristic
506C23×C4C2411yescharacteristic
507C23×C4C2411yescharacteristic
508C23×C4C2411yescharacteristic
509C23×C4C2412yes—
510C4⋊Q8—216no—
511#127—232no—
512#127—232no—
513#127—216no—
514#127—216no—
515#127—48no—
516#127—48no—
517#126—216no—
518#126—216no—
519#126—216no—
520#125—216no—
521#125—28no—
522#124—216no—
523#124—216no—
524#124—28no—
525#124—48no—
526#124—48no—
527#123—216no—
528#123—216no—
529#123—216no—
530#123—216no—
531#123—216no—
532#123—416no—
533#123—88no—
534C22⋊Q8—28no—
535C22⋊Q8—28no—
536C22⋊Q8—28no—
537C22⋊Q8—28no—
538C22⋊Q8—28no—
539C22⋊Q8—216no—
540C22⋊Q8—416no—
541#121—216no—
542#121—216no—
543#121—28no—
544#121—28no—
545#121—28no—
546#121—28no—
547#121—28no—
548#121—216no—
549#121—28no—
550#121—28no—
551#121—216no—
552#121—28no—
553#121—28no—
554#121—232no—
555#121—232no—
556#121—232no—
557#121—232no—
558#121—216no—
559#121—416no—
560#121—432no—
561#121—816no—
562#121—816no—
563#120—216no—
564#120—216no—
565#120—416no—
566#120—416no—
567#120—416no—
568#120—88no—
569C4×Q8—216no—
570C4×Q8—216no—
571C4×Q8—28no—
572C4×D4—216no—
573C4×D4—216no—
574C4×D4—216no—
575C4×D4—232no—
576C4×D4—232no—
577C4×D4—216no—
578C4×D4—216no—
579C4×D4—28no—
580C4×D4—432no—
581C4×D4C2×D4116yes—
582C4×D4C2×D4116yes—
583C4×D4C2×D4116yes—
584C4×D4C2×D4116yes—
585#117—28no—
586#117—216no—
587#117—216no—
588#117—44no—
589#117—44no—
590C2×C4⋊C4—28no—
591C2×C4⋊C4—24no—
592C2×C4⋊C4—24no—
593C2×C4⋊C4—24no—
594C2×C4⋊C4—28no—
595C2×C4⋊C4C2×D418yes—
596C2×C4⋊C4C2412yes—
597C2×C4⋊C4C2414yes—
598C2×C4⋊C4C2412yes—
599C2×C4⋊C4C2412yes—
600C2×C4⋊C4C2418yes—
601C2×C4⋊C4C2412yes—
602C2×C4⋊C4C2412yes—
603C2×C4⋊C4C2414yes—
604C2×C4⋊C4C2412yes—
605C2×C4⋊C4C2414yes—
606C2×C4⋊C4C2414yes—
607C2×C4⋊C4C2414yes—
608C2×C4⋊C4C24116yes—
609C2×C4⋊C4C2414yes—
610C2×C4⋊C4C2414yes—
611C2×C4⋊C4C2414yes—
612C2×C4⋊C4C2418yes—
613C2×C4⋊C4C24116yes—
614C2×C4⋊C4C2412yes—
615C2×C4⋊C4C2412yes—
616C2×C22⋊C4—28no—
617C2×C22⋊C4—28no—
618C2×C22⋊C4—28no—
619C2×C22⋊C4—28no—
620C2×C22⋊C4—216no—
621C2×C22⋊C4—48no—
622C2×C22⋊C4C2×D418yes—
623C2×C22⋊C4C2×D418yes—
624C2×C22⋊C4C2414yes—
625C2×C22⋊C4C2414yes—
626C2×C22⋊C4C2414yes—
627C2×C22⋊C4C2418yes—
628C2×C22⋊C4C2414yes—
629C2×C22⋊C4C2414yes—
630C2×C22⋊C4C2414yes—
631C2×C22⋊C4C2414yes—
632C2×C22⋊C4C2414yes—
633C2×C22⋊C4C2414yes—
634C2×C22⋊C4C2414yes—
635C2×C22⋊C4C2414yes—
636C2×C22⋊C4C2414yes—
637C2×C22⋊C4C24116yes—
638C2×C22⋊C4C2414yes—
639C2×C22⋊C4C2414yes—
640C2×C22⋊C4C2418yes—
641C2×C22⋊C4C2414yes—
642C2×C22⋊C4C2414yes—
643C2×C22⋊C4C24116yes—
644C2×C22⋊C4C2414yes—
645C2×C22⋊C4C24116yes—
646C2×C22⋊C4C24116yes—
647C2×C22⋊C4C24116yes—
648C2×C22⋊C4C24116yes—
649C2×C22⋊C4C24116yes—
650C2×C22⋊C4C24116yes—
651C2×C22⋊C4C2414yes—
652C2×C22⋊C4C2412yes—
653C2×C22⋊C4C2412yes—
654C2×C22⋊C4C2412yes—
655C2×C22⋊C4C2412yes—
656C2×C42—28no—
657C2×C42—48no—
658C2×C42C2×D418yes—
659C2×C42C2414yes—
660C2×C42C2414yes—
661C2×C42C2414yes—
662C2×C42C2414yes—
663C2×C42C2418yes—
664C2×C42C2418yes—
665C2×C42C2412yes—
666C2×C42C2412yes—
667#95C2414yes—
668#95C2414yes—
669#95C2418yes—
670#95C2418yes—
671#95C2418yes—
672#95C2414yes—
673#95C2414yes—
674#95C24116yes—
675#95C24116yes—
676#95C2418yes—
677#95C24116yes—
678#95C24116yes—
679C24—24no—
680C24—24no—
681C24—24no—
682C24—24no—
683C24—24no—
684C24—28no—
685C24—28no—
686C24—42no—
687C24—42no—
688C24—44no—
689C24—44no—
690C24—42no—
691C24—42no—
692C24—44no—
693C24—44no—
694C24—44no—
695C24—44no—
696C24—44no—
697C24C22×D414yes—
698C24C22×D414yes—
699C24C2514yes—
700C24C2514yes—
701C24C2514yes—
702C24C2511yescharacteristic
703C24C2511yescharacteristic
704C24C2512yes—
705C24C2511yescharacteristic
706#41—432no—
707#41—432no—
708#41—464no—
709#41—464no—
710#41—432no—
711#41—432no—
712#41—816no—
713C2×Q8—232no—
714C2×Q8—24no—
715C2×Q8—24no—
716C2×Q8—24no—
717C2×Q8—24no—
718C2×Q8—28no—
719C2×Q8—24no—
720C2×Q8—28no—
721C2×Q8—44no—
722C2×Q8—88no—
723C2×Q8H(5,𝔽2)18yes—
724C2×D4—28no—
725C2×D4—28no—
726C2×D4—28no—
727C2×D4—216no—
728C2×D4—28no—
729C2×D4—216no—
730C2×D4—28no—
731C2×D4—28no—
732C2×D4—28no—
733C2×D4—216no—
734C2×D4—28no—
735C2×D4—216no—
736C2×D4—24no—
737C2×D4—24no—
738C2×D4—24no—
739C2×D4—24no—
740C2×D4—24no—
741C2×D4—24no—
742C2×D4—216no—
743C2×D4—28no—
744C2×D4—216no—
745C2×D4—28no—
746C2×D4—28no—
747C2×D4—24no—
748C2×D4—28no—
749C2×D4—24no—
750C2×D4—416no—
751C2×D4—44no—
752C2×D4—44no—
753C2×D4—416no—
754C2×D4—48no—
755C2×D4—44no—
756C2×D4—44no—
757C2×D4—48no—
758C2×D4—44no—
759C2×D4—44no—
760C2×D4—432no—
761C2×D4—432no—
762C2×D4—432no—
763C2×D4—416no—
764C2×D4—416no—
765C2×D4—416no—
766C2×D4—416no—
767C2×D4—416no—
768C2×D4—48no—
769C2×D4—44no—
770C2×D4—48no—
771C2×D4—48no—
772C2×D4—416no—
773C2×D4—416no—
774C2×D4—48no—
775C2×D4—416no—
776C2×D4—416no—
777C2×D4—416no—
778C2×D4—432no—
779C2×D4—88no—
780C2×D4—816no—
781C2×D4—816no—
782C2×D4—816no—
783C2×D4C22×D418yes—
784C2×D4C22×D418yes—
785C22×C4—24no—
786C22×C4—24no—
787C22×C4—28no—
788C22×C4—24no—
789C22×C4—24no—
790C22×C4—28no—
791C22×C4—24no—
792C22×C4—24no—
793C22×C4—24no—
794C22×C4—24no—
795C22×C4—24no—
796C22×C4—216no—
797C22×C4—28no—
798C22×C4—28no—
799C22×C4—216no—
800C22×C4—28no—
801C22×C4—28no—
802C22×C4—28no—
803C22×C4—28no—
804C22×C4—416no—
805C22×C4—416no—
806C22×C4—42no—
807C22×C4—42no—
808C22×C4—44no—
809C22×C4—48no—
810C22×C4—42no—
811C22×C4—44no—
812C22×C4—42no—
813C22×C4—44no—
814C22×C4—44no—
815C22×C4—42no—
816C22×C4—44no—
817C22×C4—48no—
818C22×C4—48no—
819C22×C4—48no—
820C22×C4—48no—
821C22×C4—48no—
822C22×C4—44no—
823C22×C4—44no—
824C22×C4—432no—
825C22×C4—432no—
826C22×C4C22×D414yes—
827C22×C4C22×D414yes—
828C22×C4C22×D414yes—
829C22×C4C22×D414yes—
830C22×C4C22×D418yes—
831C22×C4C22×D414yes—
832C22×C4C22×D414yes—
833C22×C4C22×D414yes—
834C22×C4C22×D414yes—
835C22×C4C22×D414yes—
836C22×C4C22×D418yes—
837C22×C4C2518yes—
838C22×C4C2518yes—
839C22×C4C2514yes—
840C22×C4C2514yes—
841C22×C4C2514yes—
842C22×C4C2514yes—
843C22×C4C2512yes—
844C22×C4C2511yescharacteristic
845C22×C4C2512yes—
846C22×C4C2512yes—
847C22×C4C2511yescharacteristic
848C22×C4C2511yescharacteristic
849C22×C4C2514yes—
850C22×C4C2511yescharacteristic
851C4⋊C4—24no—
852C4⋊C4—28no—
853C4⋊C4—24no—
854C4⋊C4—216no—
855C4⋊C4—24no—
856C4⋊C4—24no—
857C4⋊C4—24no—
858C4⋊C4—28no—
859C4⋊C4—24no—
860C4⋊C4—28no—
861C4⋊C4—28no—
862C4⋊C4—28no—
863C4⋊C4—28no—
864C4⋊C4—232no—
865C4⋊C4—44no—
866C4⋊C4—44no—
867C4⋊C4—48no—
868C4⋊C4—416no—
869C4⋊C4C22×D418yes—
870C4⋊C4C22×D418yes—
871C22⋊C4—28no—
872C22⋊C4—28no—
873C22⋊C4—28no—
874C22⋊C4—28no—
875C22⋊C4—28no—
876C22⋊C4—28no—
877C22⋊C4—28no—
878C22⋊C4—216no—
879C22⋊C4—28no—
880C22⋊C4—28no—
881C22⋊C4—28no—
882C22⋊C4—28no—
883C22⋊C4—28no—
884C22⋊C4—28no—
885C22⋊C4—28no—
886C22⋊C4—232no—
887C22⋊C4—48no—
888C22⋊C4—44no—
889C22⋊C4—44no—
890C22⋊C4—416no—
891C22⋊C4—416no—
892C22⋊C4—416no—
893C22⋊C4—44no—
894C22⋊C4—416no—
895C22⋊C4—416no—
896C22⋊C4—416no—
897C22⋊C4—416no—
898C22⋊C4—44no—
899C22⋊C4C22×D418yes—
900C22⋊C4C22×D418yes—
901C22⋊C4C22×D418yes—
902C22⋊C4C22×D418yes—
903C42—216no—
904C42—28no—
905C42—28no—
906C42—28no—
907C42—28no—
908C42—48no—
909C42C22×D418yes—
910C42C22×D418yes—
911C23—22no—
912C23—22no—
913C23—22no—
914C23—22no—
915C23—24no—
916C23—24no—
917C23—22no—
918C23—22no—
919C23—22no—
920C23—22no—
921C23—24no—
922C23—28no—
923C23—28no—
924C23—24no—
925C23—24no—
926C23—24no—
927C23—28no—
928C23—24no—
929C23—28no—
930C23—24no—
931C23—28no—
932C23—28no—
933C23—28no—
934C23—28no—
935C23—28no—
936C23—28no—
937C23—44no—
938C23—44no—
939C23—44no—
940C23—44no—
941C23—48no—
942C23—48no—
943C23—48no—
944C23—48no—
945C23—48no—
946C23—48no—
947C23—48no—
948C23—88no—
949C23—88no—
950C23—816no—
951C23—816no—
952C23—84no—
953C23—84no—
954C23—168no—
955C23C23×D412yes—
956C23C23×D414yes—
957C23C23×D412yes—
958C23C23×D412yes—
959C23#58514yes—
960C23C2611yescharacteristic
961Q8—216no—
962Q8—216no—
963Q8—48no—
964Q8—84no—
965D4—48no—
966D4—48no—
967D4—416no—
968D4—432no—
969D4—416no—
970D4—432no—
971D4—48no—
972D4—48no—
973D4—416no—
974D4—416no—
975D4—48no—
976D4—48no—
977D4—48no—
978D4—84no—
979D4—816no—
980D4—88no—
981D4—88no—
982D4—816no—
983D4—88no—
984D4—88no—
985D4—832no—
986D4—1616no—
987C2×C4—216no—
988C2×C4—24no—
989C2×C4—24no—
990C2×C4—22no—
991C2×C4—22no—
992C2×C4—22no—
993C2×C4—24no—
994C2×C4—24no—
995C2×C4—24no—
996C2×C4—28no—
997C2×C4—28no—
998C2×C4—28no—
999C2×C4—28no—
1000C2×C4—216no—
1001C2×C4—24no—
1002C2×C4—24no—
1003C2×C4—24no—
1004C2×C4—24no—
1005C2×C4—28no—
1006C2×C4—28no—
1007C2×C4—28no—
1008C2×C4—28no—
1009C2×C4—28no—
1010C2×C4—28no—
1011C2×C4—28no—
1012C2×C4—28no—
1013C2×C4—28no—
1014C2×C4—28no—
1015C2×C4—44no—
1016C2×C4—44no—
1017C2×C4—48no—
1018C2×C4—44no—
1019C2×C4—44no—
1020C2×C4—44no—
1021C2×C4—432no—
1022C2×C4—416no—
1023C2×C4—416no—
1024C2×C4—48no—
1025C2×C4—48no—
1026C2×C4—88no—
1027C2×C4—88no—
1028C2×C4—84no—
1029C2×C4—84no—
1030C2×C4—816no—
1031C2×C4C23×D414yes—
1032C2×C4C23×D414yes—
1033C2×C4C23×D414yes—
1034C2×C4C23×D412yes—
1035C2×C4C23×D412yes—
1036C2×C4C23×D412yes—
1037C2×C4C23×D412yes—
1038C2×C4C2×H(5,𝔽2)18yes—
1039C2×C4C2×H(5,𝔽2)14yes—
1040C22—22no—
1041C22—22no—
1042C22—28no—
1043C22—22no—
1044C22—24no—
1045C22—22no—
1046C22—22no—
1047C22—24no—
1048C22—22no—
1049C22—22no—
1050C22—22no—
1051C22—24no—
1052C22—48no—
1053C22—44no—
1054C22—44no—
1055C22—44no—
1056C22—44no—
1057C22—44no—
1058C22—44no—
1059C22—44no—
1060C22—44no—
1061C22—416no—
1062C22—416no—
1063C22—48no—
1064C22—48no—
1065C22—44no—
1066C22—44no—
1067C22—44no—
1068C22—88no—
1069C22—88no—
1070C22—816no—
1071C22—816no—
1072C22—168no—
1073C22#344914yes—
1074C22C24×D411yescharacteristic
1075C22C22×H(5,𝔽2)12yes—
1076C22C2×#58512yes—
1077C22H(7,𝔽2)12yes—
1078C4—24no—
1079C4—22no—
1080C4—22no—
1081C4—22no—
1082C4—28no—
1083C4—24no—
1084C4—24no—
1085C4—44no—
1086C4—44no—
1087C4—44no—
1088C4—48no—
1089C4—48no—
1090C4—44no—
1091C4#348414yes—
1092C2—24no—
1093C2—42no—
1094C2—44no—
1095C2—42no—
1096C2—84no—
1097C2—84no—
1098C2—84no—
1099C2C2×#344911yescharacteristic
1100C2C2×#348411yescharacteristic
1101C2#6285211yescharacteristic
1102C2#6289914yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×#3505C2semidirect
2. C22×#550C2semidirect
3. #40605C2semidirect
4. #40601C2semidirect
5. #38093C2semidirect
6. #38089C2semidirect
7. #37683C2semidirect
8. #37681C2semidirect
9. #37614C2semidirect
10. #37451C2semidirect
11. #37450C2semidirect
12. #37232C2semidirect
13. #36706C2semidirect
14. #35355C2semidirect
15. #35305C2semidirect
16. #35250C2semidirect
17. #35246C2semidirect
18. #35078C2semidirect
19. #34987C2semidirect
20. #34738C2semidirect
21. #34057C2semidirect
23. C23×#41C22semidirect
25. C2×#553C22semidirect
26. C2×#553C22semidirect
27. C2×#552C22semidirect
28. C2×#551C22semidirect
32. C2×#550C22semidirect
33. C2×#550C22semidirect
34. C2×#548C22semidirect
35. C2×#546C22semidirect
38. C2×#536C22semidirect
39. C2×#535C22semidirect
41. C2×#532C22semidirect
43. C22×#127C22semidirect
50. C22×#121C22semidirect
51. C22×#121C22semidirect
53. C22×C4×Q8C22semidirect
55. C22×C4×D4C22semidirect
56. #2856C22semidirect
57. #2853C22semidirect
58. #2850C22semidirect
59. #2848C22semidirect
61. #2818C22semidirect
62. #2816C22semidirect
63. #2815C22semidirect
64. #2709C22semidirect
65. #2691C22semidirect
66. #2676C22semidirect
67. #2675C22semidirect
68. #2673C22semidirect
69. #2673C22semidirect
70. #2671C22semidirect
71. #2669C22semidirect
72. #2661C22semidirect
73. #2657C22semidirect
74. #2641C22semidirect
75. #2637C22semidirect
76. #2626C22semidirect
77. #2620C22semidirect
78. #2619C22semidirect
79. #2619C22semidirect
80. #2618C22semidirect
82. #2617C22semidirect
83. #2616C22semidirect
84. #2615C22semidirect
85. #2613C22semidirect
86. #2599C22semidirect
87. #2579C22semidirect
88. #2565C22semidirect
89. #2548C22semidirect
90. #2545C22semidirect
91. #2543C22semidirect
92. #2541C22semidirect
94. #2504C22semidirect
95. #2502C22semidirect
96. #2501C22semidirect
97. #2500C22semidirect
98. #2476C22semidirect
99. #2467C22semidirect
100. #2464C22semidirect
101. #2463C22semidirect
102. #2460C22semidirect
103. #2456C22semidirect
104. #2456C22semidirect
106. #2436C22semidirect
107. #2435C22semidirect
108. #2435C22semidirect
109. #2434C22semidirect
112. #2433C22semidirect
113. #2432C22semidirect
114. #2432C22semidirect
115. #2431C22semidirect
116. #2431C22semidirect
117. #2431C22semidirect
118. #2430C22semidirect
119. #2424C22semidirect
120. #2410C22semidirect
121. #2410C22semidirect
122. #2408C22semidirect
123. #2406C22semidirect
126. #2404C22semidirect
129. #2388C22semidirect
130. #2327C22semidirect
131. #2326C22semidirect
132. #2321C22semidirect
133. #2318C22semidirect
134. #2318C22semidirect
135. #2315C22semidirect
136. #2313C22semidirect
138. #2311C22semidirect
139. #2311C22semidirect
141. C4×#120C22semidirect
142. #2297C22semidirect
143. #2290C22semidirect
144. #2290C22semidirect
145. #2283C22semidirect
148. C2×C4×C22⋊C4C22semidirect
268. C2×C4×D4D4semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#35052
C22×#5502
#406052
#406012
#380932
#380892
#376832
#376812
#376142
#374512
#374502
#372322
#367062
#353552
#353052
#352502
#352462
#350782
#349872
#347382
#340572